NASA Technical Reports Server (NTRS) 20010014196: Predicting the Rotor-Stator Interaction Acoustics of a Ducted Fan Engine

16 Pages·0.79 MB·English

by  NASA Technical Reports Server (NTRS)

AIAA 2001-0664
Predicting the Rotor-Stator Interaction
Acoustics of a Ducted Fan Engine
Robert T. Biedron
Christopher L. Rumsey
NASA Langley lqesearch Cellter, Hamilton, \'irginia
Gary G. Podboy
NASA Glenn lqesearch Center, Cleveland, OH
M. H. Dunn
Old Dominion University, Norfolk. \'irginia
39th AIAA Aerospace Sciences
Meeting & Exhibit
8-11 January 2001/Reno, NV
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344

AIAA-2001-0664
PREDICTING THE ROTOR-STATOR INTERACTION ACOUSTICS OF A
DUCTED FAN ENGINE
Robert T. Biedron* and Christopher L. t/umsey 1"
NASA Langley Research Center
Hampton, Virginia
(;ary G. Podboy _
NASA Glenn Research (lenter
Cleveland, OH
M. H. l)unn _'
Old Dominion lrniversity
Norfolk, Virginia
Abstract star,or interaction lnodes have existed for quite some
time (see, e.g., Tyler and Sofrint), but most contpu-
A Navier-Stokes computation is performed for a
rational techniques to date rely extensively on exper-
ducted-fan configuration with the goal of predicting
imental measurements and analytical scaling tech-
rotor-stator noise generation without having _o re-
niques. Although such heuristic methods can pro-
sort to heuristic modeling. The calculated pressure
vide reasonable predictions of engine tone noise in
field in the inlet region is decoml)osed into classical
many cases, they are far from perfect and it is diffi-
infiuit,e-duct modes, which are then used in either
cult to know where to luru when they are in error.
a hybrid finite-element/Kirchhoff surface method or
On the other hand, predictions from first, principles,
boundary integral equation method to calculate the
although more expeusiw', hold the promise of offer-
far field noise. Comparisons with expemnental data
ing greater insight into and col,trol of the physical
are presented, including rotor wake surveys and far
mechanisms behind the noise general|on and propa-
field sound pressure levels for 2 blade passage De-
gation processes. As computers continue to becolne
queucy (BPF) tones.
more l)owerful and inexpensive, the greater exl)ense
1 Introduction of the first-principles approach is becoming less of
an impediment.
Tone noise in ducted fan engines, resulting from
Runtsey el a[. 2 frst explored the |lse of the first-
the interaction and response of the moving rotor-
principles approach for predictillg the one blade
blade wakes with the stat.ionary st.ator vanes, prop-
passage freqtlellCy (I 13PF) modes in all advanced
agates both forward and aft. through the duct and
ducted propeller (ADP) model. Only the forward-
radiates to the far field. This noise impacts both
propagating rhodes were considered. The Navier-
communities as well a.s passengers and crew flying
Stokes equations were solved tilne-accurately on a
in aircraft.. Theoretical models for predicting rotor-
lnoving grid with sliding patched interfaces between
*Research Scientisl, (:Oml)ut at tonal Modeling and Sinmla- the rotor and stator grids. Turbulent flow was
tion Branch. achieved through the use of a one-equation turl)u-
?Senior Flesearch Scientist. Computational Modeling and lence model with a wall fmwtion al)proach. The
Simulation Branch. Associate Fellow AIAA.
acoustic modes inside the engine were both gener-
IAerospace Engineer, Acoustics Branch, Senior IMelnber
A1AA. ated and propagated using this numerical method.
§Assistant Professor, Department of Mathematics and and a particular mode of interest was shown to prop-
Scat|sties, Member AIAA.
agate well upstream of the rotor inside the engine
Copyright @2001 by the American Institute of Aeronau-
tics and Astronautics, Inc. No copyright is asserted in the with minimal attenuation. Separate at:oust|(" (-<)des
tin|ted States under Title 17. U.S. Code. The (T.S. Govern- were used to propagate these internal results out t.o
ment has a royalty-free license to exercise all righls under the the far field.
copyright claimed herein for government purposes. All other
rights are reserved by the copyright owner. The study of Rumsey et al. dentonstrated the
1
American Institute of Aeronautics and Astronautics
feasibilityof usinga Navier-Stoke('sFD codeto
tially first-order accurate, which resulls in block-
bothgeneralaendpropagattehetoneuoisewithina
tridiagonal inversions for each sweel), tlowever, for
du('tedfallengineH. owevetrh,einitialstudywasfor
solutions that use FDS the block-tridiagonal inver-
l BPFmodesw, hichareoftenst.rongearndhence
sions are further simplified with a diagonal algo-
easietropredi('lthanhigherharmonimc odesA. lso,
rithm, qurl)ulem'e equations are solved uncouph,d
mostenginesaredesignewdith bladeCOUlltssuch
fl'om the mean equations.
thaiall1BPFmodeasrecutoff'(dol|otpropagate),
The turbulence model used is the one-equation
sointhissensteheearlierADPcasewasunrealistic.
Spalart-Alhnaras (SA) model, 4 in combination with
The
Cllrrellt sludv applies the same methodology a wall flmction approach. The wall function ap-
as fief. 2 to a more realistic case for which the 1BPF proach obtains a "pseudo"-wall viscosity thai forces
modes do not propagate but the 2 BPF modes do. the law-of-the wall to hold. Details can be found
Furthermore. more extensive experimental data is in Ref. 3. The advantage of using the wall rune-
available for this new case, including rotor wake ve- lion form is that the grid spacing does not need to
lociLy profiles between the rotor and st,ator rows, al- be as tight near the solid walls (,q+ _ 80 as op-
lowing tk)r a belier assessment of the first-tu'ineiples posed to y+ ,_ 1), so the stretching into the field is
met hod. This report details the progress and lessons less severe. This is particularly important for acous-
learned to date, with the purl)oSe of guiding fllt,ure tic coml)utations, for which good grid resolution is
computational efforts in this area. Speei[i,'all 3, rotor needed throughou! tile field t.o resolve the acoustic
wake pretties between the rotor and staler rows are pert ur bat ions.
compared with measured data. and forward-moving A sliding patched imerface ('OlllleCt.s the rotor
acoustic mode amplitudes within the duct are ana- and staler rows. At, this interface, non-conservative
lyzed. These it>duct acoustic results are then used
interpolations are used, as described in Rumsey. 5
to compute tile far field noise in Colnparison with
In this reference, an engineering rule-of-thumb was
experinmntally measured levels, using both a wave developed for determining the maximum computa-
envelope/Kirchhoff method and a boundary integral t,ional tilne step allowable so that, the acoustic waves
equation method. that pass through the interface are not distorted. We
adhere t,o this rule-of-thumb in the current work.
2 Numerical Methods
For all the computations performed in this study,
2.1 the CFLaD code was run time-accurately with three
Navier-Stokes method in interaction region r-TS subit.erations per time step performed in com-
The ('FD ('ode used in tile current investigation bination with multigrM, as described in Refs. 2 and
is ('FL:H), 3 a widely-used structured-grid upwind :{.
finite-volume method. It neglects viscous ('ross-
derivative t,erms, which results in the thin-layer 2.2 Propal4ation technique to the far field
Navier-Stokes equal ions in Sl)ecified coordinate di- In principle, the (:FD code could be used to di-
rections. Third-order upwind-biased spatial (lifter- rectly calculate the far field noise, llowever, because
('llCillg on the convective and pressure terms, and of the code is only second-order accurate, such an ap-
second-order differencing on the viscous terms are proach would require a prohibitive number of grid
used: it is globally second-order spatially accurate. points. To make the problem tractable, a hybrid
Tile ('FLaD code can solve flow over multiple-zone methodology is used that combines the modal data
grids that are ('Ollllected ill a one-to-one, l)atehed, extracted from the CFD solution with more efficient
or overset manner, and can employ grid sequencing, means of colnputing the far field noise.
multi-grid, and local lime stepping when accelerat- Two approaches are considered. In the first,, the
ing convergence to steady state. I'pwind-biased spa- modal data is inl)ut t,o Eversman's Finite Element
tial dilDrem'ing is used for the inviscid terms, and Model (FEM) duct radiation code. '_ This velocity-
flux limiting is used to obtain smooth solutions in l)otential based EEM code is then used to propagate
the vicinity of shock waves, when present. No liln- the acoustic waves away from the ilflet region; no at-
it.er was employed for this study. Viscous terms are tempt is made to include acoustic propagation from
centrally differenced. Tile flux difference-splitting the exhausl flow. While the FEM code has been
(FI)S) method of Roe is employed to obtain, fluxes found to be accurate in the near field, phase infor-
at lhe ('ell faces. matiou is not well represented m the far field. To
The ('FL:_D code is advanced in time with overcome this difficulty, a l_ir(:hhoff surface is con-
an implicit three-factor approximate factorization structed using the near field FEM solution, and a
method The implicit derivatives are written as spa- l{irchhoff integral formulation is elnployed t.o corn-
2
American Institute of Aeronautics and Astronautics
t)ut,ethenoiseat.anypointin tilefarfield. This harmonic, B is the number of rotor blades, I" is the
approachisdescribeidll detailinFief.7. Thiswas number of stator vanes, and k is zero or any positive
alsotheapproachusedill theprevioursotor-stator
or negative integer.
noisestudy.'-'
Ill the current study we are focusing on the
Thesecondapproachusestileductedfallnoise
upstrcam-moving 52BPF _tl = -6 modes (b = 2
predictioncodeTBIEM3Ds.'"_
(ising boundary in- and k = -1). All 1 BPF modes are cut-oil for this
tegral equation techniques for solving tile time har- configuration. 11 The m = -6 modes are periodic
monic convective wave equatiou, TBIEM3I) calcu- over 1/6th of the engine circumference (60°), and
lat.es the sound scattered by an infinitely thin, con- rot.ate in the direction ol*posit_ to tha! of the rotor.
stant radius cylindrical duct in a uniform axial flow These are the lowest,-order circumferential modes,
fekl. Fan noise generation is approximated by sim- and hence have the least stringent grid-spacing re-
ple spinning mouopole or dipole point and/or line quirements for the (!FD code: the higher the order
sources. In the present simulat, iou, spinning line the mode, the more points are required to accurately
sources were used to generate the eircunfferential represenl it. Given all average in-duct Mach number
lllodes of interest. The line source strengths were of M = 0.265 between the rotor and staler rows and
adjusted to match as closely as possil)le the radial .Ii = 0.2;') in front of tile rot.or, the only m = -6
mode deconlposition fl'onl the (:FD. modes that propagate upstream wit, bout decay ac-
cording to the infinite-duct theory are the first three
3 Results radial modes. The axial waveleng! hs associated with
each of these modes are: At-,;,1) = 0.087- 0.08. () In,
3.1 Description of the test case
At_<,,) = 0. 104-0.106 m, and A(-,-;.3) = 0.151-0.1")7
An advanced high byl)ass subsonic fan was de-
m. The frst number in the range represents tile
signed and built by tile Allison Engine (;ompany
under contract to NASA Glenn Research (!enter. ms wavelength associated with the higher Math nun>
bet. Note that these wavelengtl,s are theoretical val-
described by Woodward el al. 1° The fall has 18 ro-
ues for a COils*ant Macl>number infinite duct; there-
t,or blades with a diameter of 22 in. (0.559 m). and
fore they represent approximate levels expected in
42 stator vanes. In the acoustic tests performed at,
*lie engine, where the Math number varies.
NASA Glenn, various configurations of staler vanes
were used: forward radial, aft radial, swept only,
3.2 Grid size and spacing
and swept plus leaned. For tile presenl computa-
For this case. it, is necessary to have a grid that
tions, only the radial starers ill the forward posi-
covers a full 60 ° of the inside of the engine. Thus, 3
tion are considered. (In the forward i)osition, the
rotor passages and 7 staler passages must be mod-
staler leading edge is approximately 3.95 in. (0.1(l
eled for the engine with 18 blades alid 42 vanes. The
m) behind the rotor trailing edge.) The t-omputa-
tions use a fall speed of 5210 RPM, which is 50% grid for the current study is made up of these 10
zones, plus 3 addit.ional zones modeling the exterior
of the nominal design speed (approach setting), and
of the engine, out. to a far field apl)roximately 37
only forward-propagating acoustic modes are con-
sidered. The currenl computations are run using in. (0..% m) in front, 62 in. (1.57 m) al)ove, and 53
a free stream Math number of M = 0.2. This is in. (1.35 m) behind tile engine cowl (the engine cowl
is approxmlately 34.5 in. (0.88 m) long). All overall
higher than the M = 0.1 used in l'/ef. 10. }Iowever,
view of the far field grid is shown in Fig. 1. The
tile higher free st,ream Mach number t)rimarily af-
fect,s the flow external to the engine, including the grid size of each rotor passage is ::_521× 57 x 41 (these
numbers rel)resent axial, radial, and circumferential
stagnat.ion point on the cowl. The flow inside the en-
spacing, respectively). The grid size of each st,at.or
gine itself is prinlarily det,ermined by the rotor RPM
passage is 129 × 57 × :{3. There are approximately
and is not expected t.o differ significantly for the two
conditions. The Fieyno[ds numl)er is taken t.o be 4.12 x 10'_ total grid points ill the 13 zones.
4.882 x 10'_ per m. To do a reasonable job in an engine acoustic con>
With 18 rotors and 42 st,at,ors, Tyler-Sofrin infi- putation, the CFI) code has to adequately resolw _
nite duct linear t.heory I can be used t.o determine two trot)or*ant aspects of the |tow: the "creation"
the forward-moving modes that propagate. Duct. phase and the "propagation" phase. The "creation"
acoustic modes are generally characterized as (m, n) phase is tile phase that oc('urs near the staler lead-
modes by their circumferential and radial mode ing edge, where the interaction of the rotor wakes
numbers m and I_. As discussed in Fief. 1, the mode with the vanes creates the duct acot, stic modes in
number _t7 for a rotor-stator interaction can be ob- tile first, place. The "propagation" phase is the ad-
lained from m = hB + kl, where h is the BPF w'ct.ion of these modes through the flow field. The
3
American Institute of Aeronautics and Astronautics
ideabehindafirst-principleaspproacihslousethe
diffuses potential spurious reflections from tile exte-
Navier-Stokeeqsuationtsoresolvbeoththecreation
rior boundaries of the grid. (If one were to attempt
andpropagatiopnhasewsithinthehighlynonlinear
this type of computation with only an unstretched
regimeoftheenginew, heresimplerlinearacous-
internal-engine grid, the acoustic field would be con-
ticmethodasrenot
expected to be valid. Once the taminated by retlections from ttw boundary unless
aeollsl ic lnodes have been prol)agat.ed away from the special non-reflective acous(,ic I>oun(lary conditions
mini|near regions, linear acoustic methods can then were employed.)
take over and be used to determine the noise in the
Reasonably accurate resolution of the rotor wakes
far tieh[.
is necessary, because it, is their interaction with the
The grid size and spacing is a very crucial as- stator vanes that causes fhe tonal acoustic modes.
pect of an engine acoustic computation. This point To achieve high resolution, the rotor grids must be
cannot be stressed enough. To apply the current clustered near the approximate location of the wakes
tirst-principles approach to compute acoustic fea- as they convect aft.. A view of the j = 35 planes
tures, il is necessary to sutficiently resolve the acous- of one rotor and one stator passage are shown in
tic waves o[' interest as they propagate and the re- Fig. 4. The '_wa.ke cuts" of the rotor grid are ap-
gion where the acoustic modes are initially geuer- 1)roximately aligned with the local rotor direction,
ated must be line enough to adequately resolve their so the grid lines follow the approximate paths of the
creation. Several close-ups of tile grid are shown in wakes themselves. Additionally, the rotor grids ex-
Figs. ;2- 0. The grid was generated using TI(;ER. l'e tend downstream to be within 0.877 ill (0.0;2;2 l/l) of
In tile following paragraphs, we will point out, sonle the staler leading edge. As a result, the rotor wakes
import ant elements of tile grid and their relationship are ill a "'clustered-grid" region for a long distance
Io the acoustic aspects of the COmlmtation. before the wake passes through the rotor-stator in-
The grid is clustered near all solid walls, and terface, where clustering is lniuimized to iml)rove
stretches as it. moves into the interior. As mentioned inter-grid interpolatiolls.
earlier, to avoid cells that are too large {because of Initial computations with what was originally con-
too-large stretching factors), we utilize a turbulence sidered "'reasonable" axial spacing near the stator
model with a wall function and use a mininnml sl)ac- leading edge led to results in which the (-13, 1) mode
lug near walls such that tile ,q+ level at tile first grid was not captured at, all in tile "'ereat, iou'" phase. It.
i,oint from the wall averages approximately 80. The was subsequently det.ermined that considerably filler
current grid maintains fine axial spacing within the spacing is required near the star.or leading edge. A
engine from tile front of the inter to past the leading close-up of lhe stator leading edge region ill the ('ur-
edge on the staler. This axial spacing is fine enough reut grid is shown in Fig. 5. It ix still all opeu
so that there are at. least 27_- 30 points per axial quest.ion whether even finer gri(l spacing ill the re-
wavelength for each acoustic mode of interest. The gions surrounding the leading edge would signifi-
results for tile model problem studied in Ref. ,5indi- cantly benefit the prediction of the acoustic modes.
cate that thi_ is all adequate resolution, at. least for 1 Ill all of the conq)utations don_' tbr this study,
BPF modes. A view of the/,' = l planes of one rotor the rotor tip gap is crudely modeled by collapsil,g
and one staler passage is given ill Fig. ;2. (Note that ("zipping") tile rotor grid zones h_r the upper 5 grid
the figure distorts the inner cowl apparent shape, be- points. This zipping resuhs in an average tip gap
cause the grid lines sweet) circumferentially to align spacing of approximately 0.03 in. (7.13 × 10-4 m).
with the rotor angled direction.) The axial spac- which is similar to the actual tip gap measured ill the
ing is necessarily clustered in tile regions near the experiment near tile leading edge, but is over three
leading and trailing edges, but tile average spacing times larger than the tip gap measm'ed at. tile trail-
elsewhere ranges from roughly 0.05 in. (0.0013 m) to ing edge. A view of the rotor tip is shown ill Fig. 6.
0.1;2 m. (0.0031 m). Typical circumferential spacing looking afl. We originally atteml3ted to model the
ill tile rotor alld staler zones between tile two rows
actual tip gap spacings, ])ul the finer grid spacing
of blades is shown in Fig. 3. (:lustering ill tile cir- required near tile trailing edge made grid generation
cumferential direction is necessary both for the wake more ditticuh and also caused excessive Ioeal stretch-
region (see below) as well as near the blades. ing factors that we decided were best to avoid.
Ill front of the engine inlet and behind the stators.
the Navier-Stokes code is no longer used to track the 3.3 Computations
acoustic modes, so the grid is allowed to stretch ax- Conlputations were pertbrmed at, a nondimen-
ially ill tllese regions. This stretcllillg accomplishes sional time step of At' = 0.05 (nondimensional-
two objectives: it reduces the fetal grid size, and it ized by characteristic length (livided by free st ream
t
American Institute of Aeronautics and Astronautics
speed of sound). The characteristic length in the Tile first station corresponds to the LDV location
(!FD solution is 1 in. (0.0254 Ill) and the speed closest t.o the rotor while the secolld station corre-
of sound is taken as c-,,. = 340.145 m/s. I)imen- sponds t.o the LI)V location closest to the stator.
sionally, this time step corresponds with a tinle The second station is located within the slat.or zones
step of ,.__1= 3.73 × 10-'; s. The frequency of all of the computational grid. Nole lhat the LI)V data
2 BPF modes is given t)y Ix = 2Bf_/c = 57.69 was taken with the staler vanes in lhe all position,
m -1, so the time corresl>onding to one period is whereas the (TD is performed with the slat.ors in
l_, = 2rr/(('.,K) = 3.2 × 10.4 s. (A given rotor blade the forward position, ttowever, the position of the
rotates through 1 blade passage = 200 in 6.4 × 10.4 craters is not expected to significantly impact the
s.) Thus, the currenl lime stel) yields approximately rotor wakes at tile positions nleasllred. Axial veloc-
86 time steps per l>eriod for the 2 BPF modes. This ity contours at constant axial positions are shown in
nulnber exceeds the 60 recommended in Ref. 5. Figs. 9 - 12, with colnpuled contours corresponding
As a firsl phase of the computation for this case, to the fine grid. Generally speaking, the compuled
we investigate the ability of the CFD code to propa- wakes are nlucll narrower and exhibit mol;e curva-
gate a specified duct acoustic mode forward through ture than the LDV meastlreme,lls. Axial velocity
the duct. We do lhis t>3' removing the stator defect profiles at a radius of approxinmtely 8.5 in.
grid zones and specifying time-varying duct acoustic (0.216 m) are shown in Figs. la and 14, correspond-
pressures at. the exit face of the rotor grids, accord- ing to the dashed lines in Figs. 9 - 12. Although
ing to the formula: the computed width and general shape are different
from tile experiment, CFD does a reasonable job
p( r, O, x) = AJ,,, (K,. r)expi[c._ Kt -mO - 1,5_x]. (l ) capturing the depth of the rolor wake as well as the
overall trend of its evolution downstream. The axial
A is the magnitude of the perturbation, J,,, is the
velocity defects on the fine grid are not nmch differ-
Bessel function of the first, kind and order m, lf_ is
ent from tile medium grid at. the first station, but al
the radial wave number, and K_ is the axial wave
the second station the wake depth of the fine grid is
number. In essence, this computation is a check t.o
larger and in better agreement with experiment.
test whether the grid resolution is sufficient.ly fine for
the propagation part of the computation. In other We now turn to an analysis of the duct acoustic
words, given a duct acoustic mode of given strength, modes generated by the Navier-Stokes code. This is
is the given grid fine enough to propagate it forward done in a post-processing step by decomposing the
without significant attenuation to the rotor blades instantaneous pressures output by CFL3D within
(where some of the mode is scattered into different the duct into its component duct mode strengths.
frequencieQ3); and, for the part of the mode that The strength .4.of the (-6, 1) mode is shown between
survives the passage through the rotor, is the given the rotor and staler rows in Fig. 15 and ill front of
grid in front of the rot,or fine enough to l)ropagate it the rotor row in Fig. 16. Axial distances in these fig-
forward without significant attem,ation t.o the duct ures are given in t.erms of the distance forward of the
inlet? rotor stacking axis. The mode strength approaches a
As shown in Figs. 7 and 8, when an initial (-6, 1) quasi-constant level as it propagates forward toward
mode acoustic amplitude of approximately .4 = 4(1 the rotor trailing edge, and is roughly constant, after
Pa is imposed at the rear of the rotor grid, it propa- it passes through the rotor row and travels forward
gates forward t.o the trailing edge of the rotor blades through the duct. The wave-like st ructure is evident
with very little attenuation on either the lille or in both figures, and is close to the theoretical vahie
medium-level grid. Then, ronghly a third of the of A(-s.1) _ 0.09 m.
wave strength makes it through the rotors. The Note in Fig. 15 that there is no distortion ill the
wave is propagated forward on the fine grid all the acoustic signal evident near the rolor-sl.ator sliding-
way to the inlet with no attenuation, whereas on tile zone interface at a" = -0.1256 m. This lack of dis-
medium-level grid it loses a small percentage of its tortion indicates successful transfer of acoust ic infor-
strength. Therefore, the current fine grid appears mation across the patched interface, s Between the
to be line enough for the propagation of the (-6, 1) rotor and stator rows, the (-6, 1) strength from lhe
mode of interest. fine grid averages roughly 20 Pa. and in from of the
Next. we run the full prol)lenl, including the sta- rot,or row, it averages roughly 5 Pa. This 75_7_,per-
rers, and determine tile ability of the CFD code to cent, reduction in nlode strength is similar to that
successfully generate the 2 BPF modes. As a first seen ill the earlier prescribed-nmde case. There is a
step, we compare the computed rotor wakes with modest increase in magnitude of the mode st.rength
LDV data taken at NASA Glenn Research ('.enter. between the medium and fine level grids ill front
5
American hlstitute of Aeronautics and Astronautics
oftilerotor,indicatingthatfurtherrefinemenbte-
dieted far field noise levels increase I)y nearly 10 dB
yondthe
lille grid may still yield increased acoustic and are much closer io the experimental measure-
strength, t'lesults for tile (-6,2) and (-6.3)nlodes ments. Other noise-prediction methodologies ignore
in front of the rotor are shown in Figs. 17 and 1_. the transmission losses entirely. 11
The (-6.2) mode fi'om the fine grid is very weak.
with an average strength of only about 3 Pa. The Why the inlet modal strengths are imderl)redicted
(-I;.3) mode has a higher amplitude of about 10 remains an open question. It may ])e that tile inter-
action of tile rotor wakes with the statol's is nol l)re-
Pa. The wavelengths of both the (-6, 2) and (-6, 3)
modes are close to the theoretical levels. Nolo that, dieted adequately because the predicted rotor wakes
are nluch narrower than the measured wakes. This
anlong the three modes, tile (-6, 3) niode shows the
underpredietion of wake width is possibly due to ei-
most signifieam change m magidtnde between the
nlediunl and fine level grids. ther inadequate physics in the lurl)ulenee model or
under-resolution of the rotor wake vorl i('al slrll('l tire
Although not shown, as a further check on the
and its inherent unsteadiness.
acoustie computations, we st udied the mode behav-
ior at a given station m front of the rotor as a func-
Thinking in terms of a Fourier transfornl of the
tion of time. Given that the mode behavior is kine-
rotor wakes in the circumferential direction, nar-
maritally determined, we know theoretically how
rower wakes have a higher fre(lUellCV COllt.enl lhan
much it should rotate in a given number of itera-
wider wakes. Perhaps, t]lell, the comt)uted noise
lions. Results confirm that the (-6, 1) and (-6, 3)
sources are biased towards harmonics higher than
modes rotate at approximately theeorreet rate and
2 BPF. Alternatively, the k)sses that occur as the
in the correct direction. The (-6,2) mode is too
sound propagates forward through the rotors may
weak to yiehl meaningful analysis.
be exacerbated by the numerical schenle. However,
solutions obtained for two grid resolutions did not
4 Far Field Noise
show a significant variation of the modal aml)litmles
The tinal step in the ('urrent study was to use the with mesh size.
exl.racted m = -6 modal strengths in the inlet duct
forward of lilt, fan (at x = 0.12(59 m) to l)redict the
far field noise. The predicted far field directivity is 5 Sllllllllary
shown in Fig. 1.9. Note that past approximalely 60
deg., the measured levels in the experiment are ele- Performing acoustic COml)utations on full rotor-
vated due to aft-end noise, which was not included stator ducted fan configurations using the Navier-
i,/ the (TI) COmlmtation. As ('all be seen. the com- St,ekes equations is I)y no means a simple push-
t)uled sound pressure levels forward of 60 (leg. are button task. The work presented here is the see-
signiticantly lower than the experimentally measured on(I of a series of COml)utations I)erformed to as-
levels, using t)oth the FEM/Kirchhofl" approach aml sess whether Navier-Stokes solvers can t)e used to
the TBIEM3I) al)proaeh. (Note that TBIEM3I) uses directly eal)ture the SOUll.d generation nlechanisms
all idealized duct, whereas FgM/Kirchhoff uses the of rotor-staler intera('lion, wit houl resorting to nlore
act ual duct geometry. Thus, results are not exl)eeted heuristic modeling techniques. The earlier study, for
to agree: for example, TBIEM3D yields higher SPLs a configuratioll exhibiting 1 BPF tones, had a fair
at higher emission angles because of diffraction from degree of success in predicting the far field noise. In
tile idealized duct's sharp leading edge.) The cause the current study, for which the lowest order 1)ropa-
of the diserel)ancy between ('FI) and experiment is gating modes are 2 BPF, the predicted far field noise
therefore ahnost certainly related to the extracted levels are about l0 12 dB low. It was determined
modal data from the (TI) solution the ('onlputed that the l,ropagatio, within the duel of the 2 BPF
source strengths ill Ilia inlel region art' too low by modes was not as difficult as their cr_atto, via l.he
about a factor of 3-6. first-principles al)proach. The wake widths obtained
As discussed previously, there is a 65%-75(_, reduc- from the computation were considerably narrower
tion in the modal amplitudes as the waves generated than those measured ill the experiment. This may
I)y rotor-staler interaction travel forward through t)e I)e the l)ri,nary cause of the diserel)ancy in the
tile rotor and into the inlet. Although not shown, computed and measured far field noise lew_ls. Addi-
if the transnlission losses through the rotor arm ig- tional research is needed to explore in greater depth
nored, i.e.. if the modal strengths between the stator the grid and turbulence model requirements in lhe
and the rotor {e.g., Fig. 15) are used instead of those interaction region where the rotor wakes conveet all(-]
ill front of tile rotor (e.g. Fig. |6), thell tile pre- the acoustic modes are created.
(i
American lnstit.ute of Aeronautics and Astronautics
A ekm)wledgments 11. Envia. E., and Nallasamy, N., "Design Selection
and Analysis ofa Swel)t and Leaned Star.or ('on-
The authors wouhl like to thank F. Farassat of
cept ,'" NASA TM- 1.q.qb-208662, December 1998.
NASA Langley Research Center for many fruitful
discussions during the course of this work. The au- 12. Shih, M. H.. Soni, B. K.. and Janus, a.
thors also thank H. Woodward of NASA (;lenn lt('-
M., "TIGEit: Turl)omachinery Interactive Grid
search (:enter for providing tneasm'ed sound data, Generation / Flow Sinmlalion System I.rser's
and L. Heidelberg and D. tluff or NASA (;lenn lie- Manual," Mississippi Stale (Jniw,rsity Publiea-
search Center for their advice and expertise. t.ion, 1994.
References l3. Hanson. D. B., "'Coupled Two- Dimensional Cas-
1. Tyler, ,1. M. and Sofrin, T. G., "'Axial Flow cade Theory for Noise and l;nst.eady Aerody-
namics of Blade RowInteractions in Turbofans,"
(:ompressor Noise Studies," SAE Transactions,
NASA Cll-4506, 1994.
Vol. 70, 1.q62, pp. 30.q 332.
2. llumsey, C. I,., Biedron, t3. T., Farassal, F.,
and S1)en('e. P. L., "Duct.ed-Fan Engine A('oustic
Predictions I!sing a Navier-Stokes Code," Jot, r-
I_(tl of ,%umt aml ld.'atiom \:ol. 213, No. 4,
1998, pp. 6-13 664.
3. Krist. S. L.. Biedron, R. T., att(l Rumsey, (!. I,..
"('t"L:ID Iser's Manual (\:ersion ,5.0)", NASA
TM-1998-208444. June 1998.
,1. Spalarl, P. 13., and Alhnaras, S. R., "'A One-
Equation 'i'urbulence Model for Aerodynamic
Flows," La Recherche A_rospatial_, No. 1, 19.q4,
pp. 5 21. M=0.2
5. t_umsey, (:. L.. "(!omputat.ion of Acoust.ic
Waves Through Sliding-Zone Interfaces," AIAA stator zones
Journal. Vol. 35, No. 2, 1.t).q7, pl ). 263 268. rotor zones
6. lloy, I. I)., Eversman. W., and Meyer, 11. D.,
"'hnproved Finite Elemen! Modeling of the Tur-
Figure 1. Fat' field view of grid (k = 1 platte).
bofan Engine Inlet Radiation Problem," lleport
Prepared for NASA Lewis Fteseareh (!enler []n-
der (-_ontract NAS3-25.%:2, Task 10, April l,q,q3.
7. Spence, P.. "Ducted Fan Noise Prediction Us-
ing Wave Envelope Analysis and the Kirchhoff
Formula," AIAA Paper 97-1651, May 1997.
8. l)unn, M. It., "'TBIEM3D - A Computer Pro-
gram for Predicting I)ueted Fan Engine Noise,
Version 1.1." NASA/CR-.qT-206232, September
l.q.q7.
9. Dunn, *1. tt., Tweed, .1., and Farassat., F., "'The
Application of a Boundary Integral Equation
Method to t.he Prediction of ])ucl.ed Fan En-
gine Noise," .lourual of ,%und mM libralio.,
Vol. 227, No. 5. 1999, pp. 1019 1048.
10. Woodward, II. P., Elliot, D. M., Hughes, (!. E.,
and Berton, .]. ,].. "'Benefits of Swept attd Leaned
Stators for Fan Noise Heduction,'" AIAA Paper
99-0,17.9, January/ 1999.
7
American Institute of Aeronautics and Astronautics
Y
rotor-stator interface
z_x stator T.E.
stator L.E.
cowl LE. _
rotor T.E. z
rotor T.E.
rotor L.E.
stator L.E. stator T.E.
rotor L.E.
inflow
from
zone 1
hub LE.
Figure 2. View of rotor and stator grid zones (k = 1
Figure 4. View of rotor and stator grid zones (j = 35
plane).
plane).
rotorzones
stator L.E.
$tator zones
Y
Figure 3. View of rotor and star or grid zones (i =
Figure 5. Close-up view near stator leading edge
250 plane in rotor zones and i = 19 plane in stal,o|"
(j = 35 plane).
ZOlleS),
American hlstitute of Aeronautics and Ast,ronautics